Question

lga+lgb=2 lg(a-2b),求log4^(a/b)的值?

Answer 1

1）lga+lgb=2 lg(a-2b),

lgab=lg(a-2b)²

ab=(a-2b)²

a²-5ab+4b²=0

(a/b)²-5(a/b)+4=0

a/b=1或4

∵a>0,b>0,a-2b>0

∴a/b>2

∴a/b=4

∴log4^(a/b)的值为1.

2）log8^(9.8)

=lg9.8/lg8

=(2lg7+lg0.2)/3lg2

=(2lg7+lg2-1)/3lg2

=(2b+a-1)/3a